Z(x+9)(4x+2)=0

Solution for Z(x+9)(4x+2)=0 equation:

(Z+9)(4Z+2)=0

We multiply parentheses ..

(+4Z^2+2Z+36Z+18)=0

We get rid of parentheses

4Z^2+2Z+36Z+18=0

We add all the numbers together, and all the variables

4Z^2+38Z+18=0

a = 4; b = 38; c = +18;
Δ = b2-4ac
Δ = 382-4·4·18
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-34}{2*4}=\frac{-72}{8}
=-9
$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+34}{2*4}=\frac{-4}{8}
=-1/2
$